Robust stability and stabilizability of jump linear uncertain system with mode-dependent time-delays

The paper studies the class of uncertain linear systems with time-delay and Markov jump disturbance, in which the time-delay is assumed to be dependent on the system mode. An LMI-based condition for this class of system to be robustly stable is established. Sufficient conditions for the robust stabilizability under state feedback controller is developed and LMI-based methods to design state feedback are proposed. A numerical example is worked out to show the usefulness of the theoretic results.